Theorems · Theorem · commutative algebra

AdicCompletion.eval_lift_apply

∀ {R : Type u_1} [inst : CommRing R] (I : Ideal R) {M : Type u_4} [inst_1 : AddCommGroup M] [inst_2 : Module R M]
  {N : Type u_5} [inst_3 : AddCommGroup N] [inst_4 : Module R N] (f : (n : ℕ) → M →ₗ[R] N ⧸ I ^ n • ⊤)
  (h : ∀ {m n : ℕ} (hle : m ≤ n), AdicCompletion.transitionMap I N hle ∘ₗ f n = f m) (n : ℕ) (x : M),
  ↑((AdicCompletion.lift I f ⋯) x) n = (f n) x

Defined in

Mathlib.RingTheory.AdicCompletion.Basic

Cited by

0 results in Mathlib

Foundations

Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModule